Method of producing tones of a preferably substantially equal-tempered scale

ABSTRACT

A device for producing the tones of a musical scale from a single tone generator using a series-connected group of digital dividers for successively dividing the generated tone by 2n. The output pulses of selected dividers are combined in logic circuits to form the individual frequencies of the musical scale.

United States Patent [191 Franssen et al.

METHOD OF PRODUCING TONES OF A PREFERABLY SUBSTANTIALLY EQUAL-TEMPEREDSCALE Inventors: Nico Valentinus Franssen; Willem Ruiterkamp; ConrelisJohannes Van der Peet, all of Emmasingel, Eindhoven, NetherlandsAssignee: U.S. Philips Corporation, New'York,

Filed: Aug. 12, 1971 Appl. No.: 171,387

' Related U.S. Application Data Continuation of Ser. No. 797,914, Feb.10, 1969,

abandoned.

U.S. Cl 84/1-01, 84/].03, 84/].19, 84/DIG. 11

Int. Cl. Gl0h 5/00 Field of Search 84/101, L03, 1.11,

84/1.19, 1.22-1.24, DIG. 11

f 0,1, f 0,1, 0 f, r,

[111 3,743,756 [451 Jul 3,1973

[56] References Cited UNITED STATES PATENTS 3,509,454 4/1970 Gossel84/1.01 X 3,590,131 6/1971 Reyers l 84/].03 3,610,799 10/1971 Watson84/1.0l 3,610,801 10/1971 Fredkin et a1. 84/1.03 3,617,901 11/1971Franssen 84/1.01 X

Primary ExaminerRichard B. Wilkinson Assistant Examiner-Stanley J.Witkowski Attorney-Simon L. Cohen [5 7] ABSTRACT A device for producingthe tones of a musical scale from a single tone generator using aseries-connected group of digital dividers for successively dividing thegenerated tone by 2". The output pulses of selected dividers arecombined in logic circuits to form the individual frequencies of themusical scale.

14 Claims, 12 Drawing Figures PAIENIEUJHL a ma 3,743,756

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sum 2 W 6 f'g fig f c des A1 C C2 C3 fig.2

f; n H L n n FL FL L r fal FL L '5 1' [I L FL n ML FL J1 n n s INVENTORJNICO F. FRANSSEN WILLEM RUITERKAMP BY conneus J. PEET PATENTEBM 3 I9133. 743.756

INVENTOR? MCO F FRANSSEN WHLEM RUWERKAMP BY CORNEUS l PEET AGENTPATENIHNUL a ma 3.743.756

mm 6 0r 6 1 2 Ijz 1 2 fi .10 B1 B2 83 g INVENTOR: NIC O F. FRANSSE NWILLEM RUITERKAMP BY CORNELIS J. EET

AGEN

METHOD OF PRODUCING TONES OF A PREFERABLY SUBSTANTIALLY EQUAL-TEMPEREDSCALE This application is a continuation of application, Ser. No.797,914, filed Feb. 10, 1969, now abandoned.

The invention relates to a method of simultaneously producing tones of apreferably substantially equaltempered scale in an electronic musicalinstrument.

In a method known from US. Pat. No. specification 2,486,039, use is madeof a number of individually operating oscillators equal to the number oftones per octave, which oscillators are each tuned to a different pitch.The tones lying one or more octaves lower are derived by means ofdivide-by-two circuits (2-dividers) from the said 12 tones.

1t will be appreciated that detuning of one or more of these oscillatorsresults in one or more derived tones also being detuned so that theinstrument becomes false.

In the method according to the invention, this disad vantage is avoidedin that at least one signal determines the position of the scale and inthat each of the remaining tones of the octave is built up of pulsesequences obtained by continued division of the first signal.

In this application, the term frequency is employed to signify the pulserecurrence frequency, i.e., the number of pulses per second. A strictlyregular pulse sequence is no longer considered. The extent of variationof the pulse distance determines whether this pulse sequence isperceived subjectively as an acceptable tone.

This method permits the generation of of any arbitrary interval with anydesired degree of accuracy. For example, the interval of a minor secondof the equally tempered scale, which interval is equal to 12 1/21.059463, may be built up by deriving from the lowest frequency of theinterval by continued division by ten pulse sequences having frequenciesof 10, 10', 103, 10, 10 and 10 times the lowest frequency and by addingto the pulse sequences of the lowest frequency of 10 pulses each throughan adding circuit pulses of 10*, pulses of 9 pulses of 10*, 4 pulses of10", 6 pulses of 10 and 3 pulses of 10' times the lowest frequency. Thismethod starts from the octave tone of the lowest frequency and thelowest frequency is obtained therefrom by division by two. Of course, itis also possible to start from the highest frequency and to obtain thelower tones by subtracting the suitable pulse sequences through anadding circuit from the highest frequency while a combination ofaddition and subtraction may also be used. The term subtraction is to beunderstood to mean herein the addition of a negative number.

In the same manner, any arbitrary scale can be derived from onefrequency by using instead of the deci mal system another numericalsystem, for example, the ternary system, while the desired frequency canbe built up by means of the pulse sequences appearing at the outputs ofa chain of dividers by three.

In a particulary advantageous embodiment of the method according to theinvention, each subsequent pulse sequence is derived from the precedingpulse sequence by division by two. For this purpose the decimal valuesof the desired intervals are converted into values of the binary system.The following Table gives the decimal numbers for the tones of thenatural tuning followed by the binary values, the frequency of the Cbeing standardized at l.000.000.0.

1.0000000 1.000000 0000 D flat 1.066 666 6 1.000100 010 0 1.125 00001.001010 000 0 E flat 1.200000 0 1.001 1001101 E 1.250 0000 1.0100000000 F =1.333 333 3 1.0101010101 F sharp 1.406 250 0 1.011010 000 01.500 0000 1.100000 0000 Aflat =1.6000000 1.1001100110 1.666666 61.101010101 1 Bflat 1.800 0000 1.1100110011 B =l.875 0000 1.1110000000 C=2.000 0000 10.000 000 000 0 An oscillator supplies pulses having thefrequency of the C to a first divider by two, the frequency associatedwith the C occurring in the usual manner at the output of the firstdivider by two. The D flat is now built up by adding together the pulsesequences derived from an output of the first, the fifth and the ninthdividers by two. The remaining tones can be attained in the same manner.Alternatively, instead of adding pulse sequences together in the mannerdescribed, the D flat may be derived from the C pulse sequence bysubtracting the number 0.111 011 110 0 from 10.000 000 000 0. That is tosay that the pulses occurring at the outputs of the first, the second,the third, the fourth, the sixth, the seventh, the eight and the ninthdividers by two are each caused to suppress a pulse from the originalpulse sequence. It may also be advantageous to use a combination ofaddition and subtraction. The remaining tones of the scale can beobtained in an analogous mannet. This also applies to other tuningoperations, for example, the intermediate tone tuning, the intervals ofwhich are stated in the following Table in decimal and binary values.

C =1.0000000 1.0000000000 D flat 1.070 000 0 1.000100 0 D =1.11806571.0001111001 E flat 1.196 2960 1.0011001001 E 1.250 0000 1.010 0000000 F1.337 537 6 1.010 101 1010 F sharp 1.397 582 2 1.011001011 1 G 1.4953700 1.0111111011 Aflat =1.6000000 1.100110 011 0 A =1.67192191.1010110000 Bflat 1.788 9052 1.1100101000 B =1.8692125 1.1101111010 C=2.000 0000 10.000 000 0000 The 31-tone scale having a minimum intervalequal to 31 #2 1.022 611 5 and the commonly used equaltempered scalehaving a minimum interval equal to 12 {2 can also be obtained in thesame manner, from which follow the pitches relative to the frequency ofthe C standardized at 1.000 000 which are stated in the Table below.

If the above intervals should be defined with a higher or a lower degreeof accuracy, it is sufficient to increase or to decrease the number of2-dividers and to connect the required number of outputs to the addingcircuit until the desired degree of accuracy is attained.

It should be ensured that the pulses occurring at the outputs of the2-dividers and, as the case may be, the pulses of the signal of themaster oscillator never coincide. For this purpose, in a furtherembodiment of the method according to the invention, the frequencies arebuilt up of pulse sequencies the pulses of which are located each timeat least approximately midway between the pulses of the precedingdivider by two. In case the divider by two is constituted by a bistablemultivibrator, this can be achieved by deriving the control from oneoutput pulses and the desired pulses sequence from the other one.

In an embodiment of a device for carrying out the method, the output ofa master oscillator which, if required through a pulse shaper, gives offpulses having a width of at least approximately 50 percent of the periodand therefore a 50% duty factor, is connected to a chain of dividers bytwo. A first output of each divider by two is connected to the input ofthe next divider by two which divider by two supplies at least at asecond output, if required through a pulse-width convertor, pulseshaving an absolute pulse width at least substantially equal to that ofthe pulses at the input of the first divider by two,. Absolute pulsewidth is defined as the width of the narrowest positive on negativeexcursion ofa repetitive series of pulses. The second outputs of thedivider by two required for the formation of the signals of thedesiredtone are connected to the inputs of an OR circuit from the output ofwhich the desired tone can be derived. The OR circuit adds the pulsestogether. The tone is thus composed of the sum of the signals of therelevant dividers by two. In another embodiment of a device for carryingout the method, in which the tones are obtained from the differencebetween the pulse sequences of the master oscillator and the pulsesequences of the dividers by two, the output of a master oscillator,which, if required through a pulse shaper, gives off pulses having awidth at least approximately equal to 50 percent of the period, isconnected to a chain of dividers by two. A first output of each dividerby two is connected to the input of a next divider by two which dividerby two supplies at least at a second output, if required through apulse-width convertor, pulses having an absolute pulse width which issmaller than three times the period and larger than or equal to theabsolute pulse width of the pulses of the master generator,. The inputof the first divider by two is connected together with the secondoutputs of selected other dividers by two for the formation of thesignals of the desired tone to the inputs of an AND circuit from theoutput of which the desiredtone can be derived. In an advantageousembodiment of a device for carrying out the method according to theinvention, the dividers by two comprise logical circuits each providedwith a number of inputs and an output at which a voltage may occur attwo levels,. The voltage occurs at the first level if at least one ofthe voltages at the outputs has a first value, while the voltage occursat the second level if the voltages at the inputs all have a secondvalue,. The input signal is applied to a first input both of a first andof a second logical circuit. The outputs of the first and of the secondlogical circuit are connected to a first input of a third and of afourth logical circuit, respectively. The outputs of the third andfourth logical circuit, respectively are connected to a first input of afifth and of a sixth logical circuit. The outputs of the fifth and sixthlogical circuits, respectively are connected on the one hand to a firstand to a second output terminal, andon the other hand to a second inputof the first and of the second logical circuit. The outputs of the'firstand of the second logical circuit are moreover connected on the one handto a third input of the second and of the first logical circuit,respectively, and on the other hand to a second input of the fifth andof the sixth logical circuit, respectively.

The outputs of the third and of the fourth logical circuit are connectedto a second input of the fourth and of the third logical circuit,respectively. Thus, pulses are obtained having an absolute pulse widthsubstantially equal to that of the input signal.

If the dividers by two give off pulses having a pulse width of 50percent of the period, it is necessary for the absolute pulse width tobe reduced to that of the pulses at the input and the output of thefirst divider by two respectively, through a pulse-width convertor.

In another embodiment of a device for carrying out the method accordingto the invention, the pulse-width convertor comprises a logical circuitprovided with a number of inputs and an output at which a voltage mayoccur at two levels. The voltage occurs at the first level if at leastone of the voltages at the inputs has a first value, while the voltageoccurs at the second level if the voltages at the inputs all have asecond value. A first input of this circuit is connected to the input orthe output of the first divider by two and a second input to the firstoutput of that divider by two wherein pulse width conversion isnecessary. The remaining inputs of the logical circuits are connected tothe outputs of the preceding logical circuits.

In another embodiment of the device for carrying out the methodaccording to the invention, the pulse-width convertor comprises abistable element which is provided with two in uts and is switched by asignal at the first input into a first state and by a signal at thesecond input into a second state. the first input is connected, ifrequired with the interposition of an invertor stage, to the input ofthe first divider by two and the second input to a second output of thatdivider by two wherein pulse conversion is necessary. This circuitarrangement requires a smallr amount of wiring.

The pulses of the pulse sequences appearing at the outputs of the latterembodiment are not distributed regularly, which makes a verydisagreeable impression on the ear. A more regular distribution can beobtained by connecting each of the output terminals to a divider by n,where n is at least 2". The output signals of this divider by n shouldcorrespond to the tones of the highest desired octave so that the saidirregularities are reduced to a value acceptable for a listener. Sincethe frequencies of the octave tones are unambiguously determined by thefrequency of the master oscillator, in a further advantageous embodimentof a device for carrying out the method according to the invention, themaster oscillator is rendered continuously and/or stepwise detunable.Thus, the pitch of an instrument provided with these oscillators can beadapted to that of other instruments or be transposed. Moreover, thecontinuous detuning provides a possibility of obtaining special effects,for example, for imitating a Hawaiian guitar. The lower octave tones areeach time derived from the tones of the higher octave by means ofdividers by two.

The invention will now be described more fully with reference to thefollowing Figures, of which:

FIG. 1 illustrates how a tone of a given frequency can be built up ofdifferent pulse sequences,

FIG. 2 shows a circuit arrangement for obtaining the desired frequenciesby addition,

FIG. 3 shows a few associated pulse sequences,

FIG. 4 shows a similar circuit arrangement, in which the frequencies areobtained by subtraction,

FIG. 5 shows a few associated pulse sequences,

FIG. 6 shows a divider by two comprising logical circuits,

FIG. 7 shows the associated pulse sequences,

FIG. 8 shows a pulse-width convertor comprising a logical circuit, and

FIG. 9 shows the pulse sequences associated with this circuit,

FIG. 10 shows a pulse-width convertor comprising a bistable element,

FIG. llll shows the associated pulse sequences, and

FIG. 12 illustrates the improvement of the pulse distribution afterpassage of the pulse sequence through three dividers by two.

Referring now to FIG. 1, f denotes the pulse sequence at the input of afirst divider by two,f the pulse sequence at the second output of thefirst divider by two, f the pulse sequence at the second output of thesecond divider by two, f;, the pulse sequence at the second output ofthe third divider by two, fl the pulse sequence at the second output ofthe fourth divider by two and f,, the pulse sequence at the secondoutput of the fifth divider by two.

The lowest sequence illustrates how to build up the frequency indicatedby the number 1, 1010 by adding together the pulse sequences f f and13,. This pulse sequence may also be obtained, however, by subtractingthe pulse sequences f and f from the pulse sequence f,,. It can beclearly seen that the pulses of each subsequent pulse sequence arelocated at least approximately midway between the pulses of thepreceding divider by two.

FIG. 2 shows a circuit arrangement in which the various tones areobtained by adding together the various pulse sequences. The operationis as follows: the pulse sequence at the output of the master oscillator0 having a frequency f,, standardized at 10. 000 000 000 0 in the binarysystem is applied to the input of a first divider by two D,, a firstoutput of which is connected to the input of the subsequent divider bytwo D and so forth up to D Pulse sequences appear at the outputs of D ata frequency of 2"timesf at the outputs of D, at a frequency of 2' timesFo, at the outputs of D, at a frequency of 2 times F at the outputs of Dat a fre quency of 2 times F,,, and so forth up to pulse sequences atthe outputs of D at a frequency of 2"" times F The tones are now builtup by connecting each of the outputs of the dividers by two, of whichthe power of 2 in the binary number of the tone is indicated by a 1, toan input of an adding circuit in the form of an "OR" gate A at theoutput of which pulse sequences will appear corresponding to the pitchesof the desired tones. In the Figure, this is illustrated for the tones Dflat, D and B flat in the tempered tuning, the frequencies of whichrelative to the C in the binary system correspond to 1.000 0111101,].000111 1101 and 1. 1 010 000 1, respectively. For the sake ofclarity, the connections and the OR" gates for the remaining tones arenot shown. FIG. 3 shows the pulse sequences appearing at the input ofthe first divider by two D and at the outputs of the first four dividersby two D D D and D The pulses f ,f f andf, are used to control therespective dividers by two. From a second output of the respectivedividers by two are derived the signals f f f and j, which have anabsolute pulse width equal to that of the signal f at the input of thefirst divider by two D In the lowest sequence, a sum signal is indicatedhaving a frequency f, equal to 1,011 X fi. FIG. 4 shows a circuitarrangement in which the desired frequencies are obtained by subtractingpulse sequencies from the pulse sequence appearing at the input of thefirst divider by two D The circuit arrangement again comprises a masteroscillator 0 which may include a pulse shaper, the signal of said masteroscillator 0 being applied to an input of the first divider by two D afirst output of which is connected to an input of the second divider bytwo D which in turn supplies through a first output a control signal toa third divider by two D and so forth up to the last divider by two DThe signal f at the input of the first divider by two D, is moreoverapplied to an input of each of eleven adding circuits in the form of ANDgates A, each and gate A corresponding to a tone from the octave to beformed. The second outputs of the dividers by two D to D are eachconnected to an input of those AND" gates A which are associated with atone built up of the frequencies composed of pulse sequencescorresponding to the power of two associated with the relevant dividersby two. This is illustrated in the Figure for the tones G flat, G and Aflat built up of the frequencies 10-0, 101 100 0, 10-0, 100 000 001 0and 10-0, 011 010 011 0, respectively. FIG. 5 illustrates the pulsesequences at the input of the first divider by two D and at the outputsof the first four dividers by two and the difference signal f of thepulse sequence f at the input of the first divider by two D and at thesecond outputs of the second and of the fourth divider by two D and D,at a frequency of 1,011. Since these signals are applied to an AND gate,there is a possibility of the pulse sequences f being shifted due to thedelay of the pulse sequences at the output of a divider by two relativeto the pulse sequences at the input of this divider by two. This resultsin the pulses f being not entirely suppressed so that a narrow needle isleft, as shown in dotted lines. The narrow needle N is due to the stillsmall shift of the pulses f and the slightly wider needle N to that ofthe pulses f Therefore, the signal f is preferably inverted through aninvertor stage I to f so that the maximum permissible delay time of thepulses at the outputs of the divider by two is equal to the pulse widthb of the signal fl,. The resulting difference signal is indicated byf.,-,. It will be appreciated that in these circuit arrangements at adelay time equal to zero the absolute pulse width of the signals f I tof is allowed to be at the most percent of the pulse recurrence period off and at least equal to said period.

The dividers by two used in the above circuit arrangements each supplyan output pulse having an absolute pulse width equal to that of theinput pulse. Such an arrangement is shown in FIG. 6 and compriseslogical circuits each provided with a number of inputs and an output atwhich a voltage may occur at two levels, the voltage occurring at thefirst level if at least one of the voltages at the outputs has a firstvalue, while the voltage occurs at the second level if the voltages atthe inputs all have a second value. The input signal is applied to afirst input K both of a first and of a second logical circuit L, and Lrespectively. The outputs A and B of the first and of the second logicalcircuit L and L respectively, are connected to a first input of a thirdand of a fourth logical circuit L and L respectively, the respectiveoutputs C and D of logical circuits L and L, are connected to a firstinput of a fifth and of a sixth logical circuit L and L respectively,whose respective outputs E and F are connected on the one hand to afirst and a second output terminal E and F, respectively, and on theother hand to a second input of the first and of the second logicalcircuit L and L respectively. The outputs A and B of the first and ofthe second logical circuit L and L respectively, are moreover connectedon the one hand to a third input of the second and of the first logicalcircuit L and L respectively, and on the other hand to a second input ofthe fifth and of the sixth logical circuit L and L respectively. Therespective outputs C and D of the third and of the fourth logicalcircuit L and L respectively, are connected to a second input of thefourth and of the third logical circuit L and L respectively.

The truth Table associated with this circuit arrangement is as follows:

It should be obvious to those skilled in the art that each of thelogical circuits Ll through L6 is an AND gate of the inverting typecommonly referred to as a NAND, gate. FIG. 7 illustrates the voltagesoccurring at the various points of this circuit arrangement and itappears therefrom that the pulse sequences E and F have the sameabsolute pulse width as the input signal.

Since, however, not every type of divider is capable of supplying suchoutput pulses, though being capable of supplying pulses having a pulsewidth of 50% at the period, it may be required for the pulse width,before the signals are applied to the adding circuits, to be reduced tothat at the input of the first divider by two by means of a pulse-widthconvertor. FIG. 8 shows such a pulse-width convertor comprising alogical circuit L provided with a number of inputs and an output atwhich a voltage may occur at two levels, the voltage occurring at thefirst level if at least one of the voltages at the inputs has a firstvalue. The voltage occurs at the second level if the voltages at theinputs all have a second value. The first input of the logic circuit Lis connected to the input of the first divider D I by two and'to asecond input is connected to the first output of that divider requiringpulse width conversion, for example, D The remaining inputs of thelogical circuit are connected to the outputs of the preceding logicalcircuits associated with the dividers by two (D, and D requiring pulsewidth conversion.

FIG. 9 illustrates the pulse sequence f appearing at the input of thefirst divider by two D the pulse sequences f f f and f appearing at thefirst outputs of the divider by two D D D and D respectively, the pulsesequence f, formed in the logical circuit L and the pulse sequences fand f having the frequency of the output signal of the 2-dividers D, andD The desired signal f, then appears at the output of the logicalcircuit L An additional advantage of this circuit arrangement is thatthe pulses of the pulse sequences f f etc. are not delayed in time asthe leading edges of these pulses are determined by the signal at theinput of the first divider by two D,. This circuit arrangement may havethe disadvantage that a comparatively large number of connections arerequired. This is avoided in a circuit arrangement as shown in FIG. 10,in which the pulse-width convertor comprises a bistable element B, whichis provided with two inputs 1 and 2 and which is brought into a firststate by a signal at the first input 1 and into a second state by asignal at the second input 2. The first input 1 is connected with theinterposition of an invertor stage I to the input of the first dividerby two D, and the second input 2 to a second output of the divider bytwo requiring pulse width conversion, for example, D FIG. 11 shows thepulse sewuences occuring in this circuit arrangement, i.e. the pulsesequence f at the input of the first divider by two D,, the pulsesequence]; at the output of the invertor stage I and hence at the firstinputs of the bistable elements 8,, B, and B and the pulse sequences atthe outputs of the divider by two D,, D and D and at the second inputs 2of the bistable elements 3,, B and B and the output signals f,', f f, ofsaid bistable elements. The trailing edge of the output signal of thebistable elements B, is determined by the leading edge of the signalf,so that any time delays in the dividers are neutralized up to themaximum pulse width of the original signal.

Irregular pulse sequences appear at the outputs of all these addingcircuits, which makes a very disagreeable impression on the ear. Whenthese signals are applied to a further chain of dividers, thedistribution of these pulses becomes gradually more regular, as shown inFIG. 12. In this Figure, the pulse sequence f is a pulse sequence whichmay actually occur, for example, the sum signal f, of FIG. 3. The pulsesequence f, shows the pulse sequence f after passage through a firstdivider by two by the pulse sequence f, after passage through a seconddivider by two and the pulse sequence f after passage through a thirddivider by two. It appears therefrom that the irregularities havestrongly decreased; the pulse width ratio in the pulse sequence f whichin this case varies from 1 l to l 3, has now been reduced to a maximumvalue of 1 2 and 4 7 respectively. In FIGS. 2 and 4, these dividers aredenoted by C C etc.

In the circuit arrangements of FIGS. 2 and 4, the oscillator 0 iscontinuously and stepwise detunable. By choosing each detuning step tobe equal to half a tone, a transposition can be carried out in a simplemanner. Due to the continuous detuning, the pitch of the whole apparatuscan be accurately adapted to that of other instruments with which it maybe played. In addition, this detuning provides the possibility ofobtaining special effects, for example, the imitation of a Hawaiianguitar, in that detuning takes place over a given range each time when akey is depressed.

What is claimed is: i

l. A method of simultaneously producing all the tones of a musicalscale, comprising the steps of generating a first tone at least as highas the highest required tone, dividing the first tone by a plurality ofdifferent factors, each equal to 2", where n is an integer whilemaintaining the absolute pulse width of each divided tone equal to theabsolute pulse width of the first generated tone, thereby forming aplurality of pulse sequences, and combining selected groups of the pulsesequences as a sequence of individual pulses equal to the algebraic sumof the sequences of individual pulses within a selected group to producefrom each combined group a single tone of the musical scale.

2. A method as claimed in claim 1, wherein the step of combiningselected groups of the pulse sequences comprises adding the pulsesequence of the selected groups.

3. A method as claimed in claim 1, wherein the step of dividingcomprises dividing the frequency of the generated first tone by a factorof two to form a first pulse sequence, and dividing the frequencies ofeach formed pulse sequence by a factor of two to form the plurality ofpulse sequences.

4. A method as claimed in claim 3, wherein the step of dividing thefrequencies of each formed pulse sequence further comprises positioningwith respect to time the pulses of each pulse group, approximatelymidway between two adjacent pulses of the pulse group having the nexthighest frequency.

5. A device for simultaneously producing all the tones of a musicalscale, comprising means for generating a first pulse sequence having aconstant frequency at least as high as the highest tone of the scale,each pulse of the first pulse sequence having a pulse widthapproximately equal to 50 percent of the period thereof, a plurality offrequency divider means connected to the pulse sequence generator forproviding an output frequency equal to one half that of the inputfrequency and an output absolute pulse width equal to the absolute pulsewidth of the first pulse sequence, means for connecting the dividers inseries with an output of each divider connected to an input of anotherdivider, a plurality of or-gates each corresponding to a tone of themusical scale, and means for connecting the equal absolute pulse widthoutputs of different groups of selected dividers to inputs ofcorresponding or-gates, thereby forming pulse trains corresponding tothe tones of the scale at the outputs of the or-gates.

6. A device as claimed in claim 5, wherein each of said dividerscomprises six AND-gates, means for connecting the input of the dividerto inputs of the first and second AND-gates, means for cross-couplingthe first and second AND-gates, means for connecting the output of thefirst AND-gate to inputs of the third and fifth AND-gates, means forconnecting the output of the second AN D-gate to inputs of the fourthand sixth AND-gates, means for cross-coupling the third and fourthAND-gates, means for connecting the output of the third AND-gate to aninput of the fifth AND-gate, means for connecting the output of thefourth AND- gate to an input of the sixth AND-gate, means for connectingthe output of the fifth AND-gate to an input of the first AND-gate,means for connecting an output of the sixth AND-gate to an input of thesecond AND- gate, means for connecting the output of the fifth AND-gateto an output terminal of the divider, and means for connecting theoutput of the sixth AND-gate to a second output terminal of the divider.

7. A device as claimed in claim 5, wherein the frequency of the meansfor generating the first pulse sequence is equal to N times the highesttone of the scale, and further comprising a separate digital dividerhaving a division factor of N connected to the output of each or-gate.

8. A device as claimed in claim 5, wherein the means for generating thefirst pulse sequence is continuously and step wise detunable.

9. A musical instrument provided with a device as claimed in claim 5.

10. A device as claimed in claim 5, wherein the serially connectedoutput of each divider means provides an output frequency equal to onehalf the frequency on the input terminal thereof and an output absolutepulse width equal to the input period, and wherein each divider meansfurther comprises a pulse width converter means connected to the meansfor generating the first pulse sequence for reducing the absolute pulsewidth of each divider means to approximately the absolute pulse width ofthe first pulse sequence.

11. A device as claimed in claim 10, wherein the pulse width convertermeans comprises a separate AND-gate corresponding to each divider meansand having an input terminal connected to the serially connected outputterminal of each corresponding divider means, each AND-gate having asecond input terminal connected to the means for generating the firstpulse sequence, and means for connecting an output of each AND-gate toan input terminal of each AND-gate corresponding to a lower frequency,the outputs of each AND-gate comprising a pulse series, each having anabsolute pulse width equal to one half the period of the first pulsesequence.

12. A device as claimed in claim 10, wherein each pulse widthconvertermeans comprises a bistable device switchable to a first stablestate in response to an input pulse on a first input thereof andswitchable to a second stable state in response to a pulse on a secondinput thereof, means for connecting an output of each divider to thesecond input of a corresponding bistable element, and means forconnecting the pulses of the first pulse sequence to the first input ofeach bistable element.

13. A device for simultaneously producing all the tones of a musicalscale, comprising means for generating a first pulse sequence having aconstant frequency at least as high as the highest tone of the scale,each pulse of the first pulse sequence having a pulse width ofapproximately 50% of the period thereof, a plurality of frequencydividers each having an output frequency equal to one half that of theinput frequency applied thereto and having an output absolute pulsewidth smaller than percent of the period of the first pulse sequence andat least as large as the absolute pulse width of the input pulsesapplied thereto, means for connecting the dividers in series with theoutput of each divider connected to the input of a different divider,and logic circuits corresponding to each tone of the musical scale, andmeans for connecting the outputs of different groups of dividers to theinputs of corresponding logic circuits, thereby forming pulse trainscorresponding to the tones of the scale at the output of the logiccircuits.

14. A device as claimed in claim 13, wherein each of said dividerscomprises six AND-gates, means for connecting the input of the dividerto inputs of the first and second AND-gates, means for cross-couplingthe first and second AND-gates, means for connecting the output of thefirst AND-gate to inputs of the third and fifth AND-gates, means forconnecting the output of the second AND-gate to inputs of the fourth andsixth AND-gates, means for cross-coupling the third and the sixthAND-gate to an input of the second AND- gate, means for connecting theoutput of the fifth AND-gate to an output terminal of the divider, andmeans for connecting the output of the sixth AND-gate to a second outputterminal of the divider.

1. A method of simultaneously producing all the tones of a musicalscale, comprising the steps of generating a first tone at least as highas the highest required tone, dividing the first tone by a pluraLity ofdifferent factors, each equal to 2n, where n is an integer whilemaintaining the absolute pulse width of each divided tone equal to theabsolute pulse width of the first generated tone, thereby forming aplurality of pulse sequences, and combining selected groups of the pulsesequences as a sequence of individual pulses equal to the algebraic sumof the sequences of individual pulses within a selected group to producefrom each combined group a single tone of the musical scale.
 2. A methodas claimed in claim 1, wherein the step of combining selected groups ofthe pulse sequences comprises adding the pulse sequence of the selectedgroups.
 3. A method as claimed in claim 1, wherein the step of dividingcomprises dividing the frequency of the generated first tone by a factorof two to form a first pulse sequence, and dividing the frequencies ofeach formed pulse sequence by a factor of two to form the plurality ofpulse sequences.
 4. A method as claimed in claim 3, wherein the step ofdividing the frequencies of each formed pulse sequence further comprisespositioning with respect to time the pulses of each pulse group,approximately midway between two adjacent pulses of the pulse grouphaving the next highest frequency.
 5. A device for simultaneouslyproducing all the tones of a musical scale, comprising means forgenerating a first pulse sequence having a constant frequency at leastas high as the highest tone of the scale, each pulse of the first pulsesequence having a pulse width approximately equal to 50 percent of theperiod thereof, a plurality of frequency divider means connected to thepulse sequence generator for providing an output frequency equal to onehalf that of the input frequency and an output absolute pulse widthequal to the absolute pulse width of the first pulse sequence, means forconnecting the dividers in series with an output of each dividerconnected to an input of another divider, a plurality of or-gates eachcorresponding to a tone of the musical scale, and means for connectingthe equal absolute pulse width outputs of different groups of selecteddividers to inputs of corresponding or-gates, thereby forming pulsetrains corresponding to the tones of the scale at the outputs of theor-gates.
 6. A device as claimed in claim 5, wherein each of saiddividers comprises six AND-gates, means for connecting the input of thedivider to inputs of the first and second AND-gates, means forcross-coupling the first and second AND-gates, means for connecting theoutput of the first AND-gate to inputs of the third and fifth AND-gates,means for connecting the output of the second AND-gate to inputs of thefourth and sixth AND-gates, means for cross-coupling the third andfourth AND-gates, means for connecting the output of the third AND-gateto an input of the fifth AND-gate, means for connecting the output ofthe fourth AND-gate to an input of the sixth AND-gate, means forconnecting the output of the fifth AND-gate to an input of the firstAND-gate, means for connecting an output of the sixth AND-gate to aninput of the second AND-gate, means for connecting the output of thefifth AND-gate to an output terminal of the divider, and means forconnecting the output of the sixth AND-gate to a second output terminalof the divider.
 7. A device as claimed in claim 5, wherein the frequencyof the means for generating the first pulse sequence is equal to N timesthe highest tone of the scale, and further comprising a separate digitaldivider having a division factor of N connected to the output of eachor-gate.
 8. A device as claimed in claim 5, wherein the means forgenerating the first pulse sequence is continuously and step wisedetunable.
 9. A musical instrument provided with a device as claimed inclaim
 5. 10. A device as claimed in claim 5, wherein the seriallyconnected output of each divider means provides an output frequencyequal to one half the frequency on the input Terminal thereof and anoutput absolute pulse width equal to the input period, and wherein eachdivider means further comprises a pulse width converter means connectedto the means for generating the first pulse sequence for reducing theabsolute pulse width of each divider means to approximately the absolutepulse width of the first pulse sequence.
 11. A device as claimed inclaim 10, wherein the pulse width converter means comprises a separateAND-gate corresponding to each divider means and having an inputterminal connected to the serially connected output terminal of eachcorresponding divider means, each AND-gate having a second inputterminal connected to the means for generating the first pulse sequence,and means for connecting an output of each AND-gate to an input terminalof each AND-gate corresponding to a lower frequency, the outputs of eachAND-gate comprising a pulse series, each having an absolute pulse widthequal to one half the period of the first pulse sequence.
 12. A deviceas claimed in claim 10, wherein each pulse width converter meanscomprises a bistable device switchable to a first stable state inresponse to an input pulse on a first input thereof and switchable to asecond stable state in response to a pulse on a second input thereof,means for connecting an output of each divider to the second input of acorresponding bistable element, and means for connecting the pulses ofthe first pulse sequence to the first input of each bistable element.13. A device for simultaneously producing all the tones of a musicalscale, comprising means for generating a first pulse sequence having aconstant frequency at least as high as the highest tone of the scale,each pulse of the first pulse sequence having a pulse width ofapproximately 50% of the period thereof, a plurality of frequencydividers each having an output frequency equal to one half that of theinput frequency applied thereto and having an output absolute pulsewidth smaller than 150 percent of the period of the first pulse sequenceand at least as large as the absolute pulse width of the input pulsesapplied thereto, means for connecting the dividers in series with theoutput of each divider connected to the input of a different divider,and logic circuits corresponding to each tone of the musical scale, andmeans for connecting the outputs of different groups of dividers to theinputs of corresponding logic circuits, thereby forming pulse trainscorresponding to the tones of the scale at the output of the logiccircuits.
 14. A device as claimed in claim 13, wherein each of saiddividers comprises six AND-gates, means for connecting the input of thedivider to inputs of the first and second AND-gates, means forcross-coupling the first and second AND-gates, means for connecting theoutput of the first AND-gate to inputs of the third and fifth AND-gates,means for connecting the output of the second AND-gate to inputs of thefourth and sixth AND-gates, means for cross-coupling the third andfourth AND-gates, means for connecting the output of the third AND-gateto an input of the fifth AND-gate, means for connecting the output ofthe fourth AND-gate to an input of the sixth AND-gate, means forconnecting the output of the fifth AND-gate to an input of the firstAND-gate, means for connecting an output of the sixth AND-gate to aninput of the second AND-gate, means for connecting the output of thefifth AND-gate to an output terminal of the divider, and means forconnecting the output of the sixth AND-gate to a second output terminalof the divider.